Generally, products such as automobiles have been financed through a personal loan system, whereby the purchaser makes a down payment, takes title to the product and pays the loan balance in monthly payments which amortize the full amount of the loan. More recently, leasing arrangements have been introduced whereby the lessee makes monthly rental payments, returning the product to the lessor at the end of a predetermined term specified in the lease. Title to the product remains in the lessor. It is sometime specified in the lease that the lessee may at his option purchase the product for a stated value when the lease expire. The conditions of the lease may also include charges, e.g. a charge for abnormal mileage or wear and tear for lease of automobile.
U.S. Pat. No. 4,736,294 discloses data processing methods and apparatus for managing vehicle financing. The data processing system provides information to assist in granting a loan, and determining at the time of making the loan a residual value of the vehicle at a predetermine option date.
Considering vehicle leases, at the signing of a lease, lessee chooses a vehicle and states how many years he intends to keep it and the approximate mileage he intends to cover. Generally speaking, the lease duration is comprised between 1 to 4 years while the number of miles varies from 20,000 to 60,000. Depending upon the vehicle and lease duration and mileage, the lessor determines monthly rental payments at the time of making the lease by estimating the resale value factor at the end of the lease, also referred to as residual value factor, and costs due to the benefit margin, insurance and maintenance. Without taking into account the margin of the lessor, insurance, maintenance, and so forth, for sake of clarity, the sum of monthly rental payments corresponds to the difference between the sticker price, i.e. the purchasing price of the automobile as proposed by the manufacturer, and the resale price. If the resale price at the end of the lease is less than the estimation done at the time of making the lease, monthly rental payments have been underestimated and, as a consequence, the lessor loses money. Reciprocally, if the resale price at the end of the lease is more than the estimation done at the time of making the lease, monthly rental payments are overestimated and thus, the leases are not attractive. During the lease, lessee may modify it to adapt its duration or mileage if the lessor agrees. In such a case, the residual value has to be reevaluated to adjust monthly rental payment accordingly.
Residual price estimation is thus critical since it could lead to lessor financial losses or unattractive commercial offers. Generally, residual price (RP) is expressed as a function of the sticker price (SP) such as,RP=α×SP  (1)
where α is the residual value factor, referred to as RV in the following description, expressed as a percentage to be applied on the sticker price. Residual value factor depends mainly on the lease conditions, e.g. lease duration and mileage. However, the influence of unforeseeable external parameter such as vehicle popularity at the end of the lease, leads to the use of approximate residual value factor that are often determined experimentally by specialists.